The testing of mechanical properties of materials, such as small articles or macro-scale samples such as soil, is a well-studied art. For relatively small-scale articles, standard tests exist for measuring mechanical properties such as Young's modulus, strain hardening exponent, yield strength, hardness, and the like, and the mechanical properties of many materials have been carefully characterized.
One set of techniques for determining mechanical properties in materials involve tests in the macro regime in which, for example, a sample of material is stretched and its overall mechanical response inferred in terms of stress and deformation. These techniques, however, typically are destructive of those samples.
Accordingly, essentially non-destructive techniques for analysis of small-scale samples such as miniaturized semiconductor articles, thin coatings for optical, electronic, magnetic, and mechanical devices, and the like have been developed. Some of these techniques involve in situ testing of mechanical properties in small-scale structures. Properties of individual phases, grain boundaries, and interfaces between phases and properties of novel materials such as nanocrystalline materials, or laminated or fibrous composites have been probed.
Indentation testing is a well-accepted technique for such testing that can be essentially non-destructive, and can be applied at a variety of scales, from nano- to macro-scale. The technique typically involves placing a sample to be tested on a stage and applying a load to a surface of the sample via an indenter so as to slightly deform or penetrate the surface, followed by removal of the load. Several techniques can be employed to derive certain properties of the material from characteristics of the interaction of the indenter with the material. One set of techniques involves measuring an area of indentation during or after indentation, for example, optically, refractively, via surface profilometry, etc. U.S. Pat. Nos. 4,627,096 (Grattoni, et al.), 4,945,490 (Biddle, Jr. et al.), 5,284,049 (Fukumoto), 5,355,721 (Las Navas Garcia), 5,483,621 (Mazzoleni), 5,486,924 (Lacey), 4,852,397 (Haggag), 5,490,416 (Adler), 3,822,946 (Rynkowski), and others follow this procedure. For example, the measured area of indentation can be used to determine a simple "flow" or hardness value for the material, which is defined as the load applied divided by the projected area of the indentation. Or, the dimension of any cracks formed in the sample surface can be measured to determine the toughness of the material. Alternatively, the depth of penetration of the indenter as a function of applied load can be measured, and calculations performed to estimate roughly some mechanical properties.
Various shapes of indenters, for example spherical, cone-shaped, and pyramidal geometries can be used in indentation testing. Sharp indenters (e.g., cone-shaped and pyramidal) can be used in conventional tests to apply a load to a sample surface to form an imprint, or until the surface cracks, followed by measurement of the area of imprint or determination of the crack length to measure hardness or toughness, respectively. One piece of indentation testing equipment utilizing a sharp indenter at ultra low loads is sold by Nano Instruments, Inc. as the Nanoindenter.TM. indentation tester. The Nanoindenter.TM. indentation tester is a relatively complex, self-contained unit including an indenter system, a sharp indenter, a light optical microscope, a moveable x-y table, and a computer. Analysis of load/depth curves with loads of less than one Newton and displacement of less than one .mu.m using a three-sided pyramidal indenter is most typically performed.
Blunt indenters, for example those having a surface contacting the sample surface that is spherical, are advantageous for use in indentation testing under certain circumstances for several reasons. First, less sample-destructive analyses often can be carried out. However, with blunt (spherical) indenters, sensitivity problems are maximized since displacement of the sensor into the sample surface, at a particular applied load, is less than displacement with a sharp indenter. This is especially problematic in measuring very soft materials. Spherical indenters have, therefore, found most use in techniques in which load is applied to a sample surface and the diameter of the indentation formed thereby is measured using, for example, optical means.
A variety of U.S. Patents, including U.S. Pat. Nos. 4,820,051 (Yanagisawa, et al.); 4,627,096 (Gattoni, et al.); 4,699,000 (Lashmore, et al.); 5,133,210 (Lesko, et al.); 5,490,416 (Adler); and 4,852,397 (Haggag) describe techniques that involve indenting a sample and determining, in a variety of ways, load, depth of penetration, and/or area of contact between the indenter and the sample during the test. In some cases an optical mechanism determines the penetration depth of the indenter and/or the area of contact between indenter and sample. In some cases, during determination of area of contact, it is assumed for simplicity that no pile-up or sinking-in of the material at the contact perimeter occurs (which is known to be a factor that must be taken into account for accurate measurement). Typically, in these techniques, the area of the indentation formed while load is applied either is not made precisely, or requires relatively complicated apparatus. In some cases, relatively time-consuming and labor-intensive processes are carried out involving multiple indentation tests made where the profile of the indentation is traced after each test with a surface analyzer to determine the depth and diameter of the indentation.
Accurate determination of the area of an indentation formed during indentation testing, especially during loading, can be critical to accurate determination of several mechanical properties of a sample. Most of these techniques also cannot accurately determine properties of a sample in the elastic and plastic regimes within a single test.
Co-pending, commonly-owned, U.S. patent application Ser. No. 08/632,665, of Suresh, Alcala, and Giannakopoulos, filed Apr. 15, 1996 and entitled, "DEPTH SENSING INDENTATION MECHANISM AND METHODOLOGY FOR MECHANICAL PROPERTY MEASUREMENTS, describes an improved technique allowing simple, reproducible, relatively uncomplicated, inexpensive, and accurate measurement of a variety of mechanical properties in a single test or series of tests on homogeneous materials. The technique involves deriving, from a load/depth relationship from an indentation test, an area of contact between the indenter and the sample during penetration without observing the area of contact during or after penetration. The area determined takes into account the area of contact due to pile-up of sample material around the indenter or sinking-in of the material. In situ load/displacement measurement, using a variety of indenter shapes and sizes, is possible in this technique.
The above techniques provide useful data for a variety of purposes, for homogeneous materials but not for functionally graded materials. Yet simplification of testing of a variety of materials at a variety of size scales would be advantageous. Accordingly, it is an object of the present invention to provide a simplified technique for indentation testing that is accurate, and is applicable to a wide variety of materials, over a variety of size scales.